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At least 181 records · Page 10

An Efficient Scheme for Updating Sparse Cholesky Factors

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Raghavan, Padma↗

Elastic-plastic stress concentrations around crack-like notches in continuous fiber reinforced metal matrix composites

Continuous fiber silicon-carbide/aluminum composite laminates with slits were tested statically to failure. Five different layups were examined: (0) sub 8, (0 sub 2/ + or - 45) sub s, (0/90) sub 2s), (0/ + or - 45/90 sub s), and (+ or - 45) sub 2s. Either a 9.5 or a 19 mm slit was machined in the center of each specimen. The strain distribution ahead of the slit tip was found experimentally with a series of strain gages bonded ahead of the slit tip. A three-dimensional finite element program (PAFAC) was used to predict the strain distribution ahead of the slit tip for several layups. For all layups, except the (0) sub 8, the yielding of the metal matrix caused the fiber stress concentration factor to increase with increasing load. This is contrary to the behavior seen in homogeneous materials where yielding causes the stress concentration to drop. For the (0) sub 8 laminate, yielding of the matrix caused a decrease in the fiber stress concentration. The finite element analysis predicted these trends correctly.

Johnson, W. S.↗

Elastic-plastic stress concentrations around crack-like notches in continuous fiber reinforced metal matrix composites

Continuous fiber silicon-carbide/aluminum composite laminates with slits were tested statically to failure. Five different layups were examined: (0) sub 8, (0 sub 2/ + or - 45) sub s, (0/90) sub 2s), (0/ + or - 45/90 sub s), and (+ or - 45) sub 2s. Either a 9.5 or a 19 mm slit was machined in the center of each specimen. The strain distribution ahead of the slit tip was found experimentally with a series of strain gages bonded ahead of the slit tip. A three-dimensional finite element program (PAFAC) was used to predict the strain distribution ahead of the slit tip for several layups. For all layups, except the (0) sub 8, the yielding of the metal matrix caused the fiber stress concentration factor to increase with increasing load. This is contrary to the behavior seen in homogeneous materials where yielding causes the stress concentration to drop. For the (0) sub 8 laminate, yielding of the matrix caused a decrease in the fiber stress concentration. The finite element analysis predicted these trends correctly.

Johnson, W. S.↗

A Structural and Molecular Approach for the Study Biomarkers

Investigation of the nucleation and growth of crystals in both abiotic and biotic systems is critical to seemingly diverse disciplines of geology, biology, environmental science, and astrobiology. While there are abundant studies devoted to the determination of the structure and composition of inorganic crystals, as well as to the development of thermodynamic and kinetic models, it is only recently that research efforts have been directed towards understanding mineralization in biological systems (i.e., biomineralization). Biomineralization refers to the processes by which living organisms form inorganic solids. Studies of the processes of biomineralization under low temperature aqueous conditions have focused primarily on magnetite forming bacteria and shell forming marine organisms. Many of the biological building materials consist of inorganic minerals (calcium carbonate, calcium phosphate, silica or iron oxide) intricately combined with organic polymers (like proteins). More recently, efforts have been undertaken to explore the nature of biological activities in ancient rocks. In the absence of well-preserved microorganisms or genetic material required for the polmerase chain reaction (PCR) method in molecular phylogenetic studies, using biominerals as biomarkers offers an alternative approach for the recognition of biogenic activity in both terrestrial and extraterrestrial environments. The primary driving force in biomineralization is the interaction between organic and inorganic phases. Thus, the investigation of the ultrastructure and the nature of reactions at the molecular level occurring at the interface between inorganic and organic phases is essential to understanding the processes leading to the nucleation and growth of crystals. It is recognized that crystal surfaces can serve as the substrate for the organization of organic molecules that lead to the formation of polymers and other complex organic molecules, and in discussions of the origins of life, is referred to as organic synthesis on mineral surfaces. Furthermore, it is suggested that the interaction between mineral surfaces and simple organic molecules resulted in the formation of amino acids, RNA, and perhaps other more complex molecules such as proteins. On the other hand, in natural systems, it is recognized that functional groups on cell walls or membranes of microorganisms serve as sites of nucleation and crystallization. The precise replication of biominerals with controlled structure, morphology, size and texture is not confined to higher organisms as it also occurs in primitive prokaryotic cells such as magnetotactic bacteria and cyanobacteria. This suggests that the principal strategies of biomineralization were established early on in the evolutionary history of organisms. It is critical, therefore, to search for common mechanisms within diverse biological systems. One such common factor is the capability for organization and self-assembly. Organic macromolecules such as proteins and lipids can aggregate and polymerize forming membranes or extracellular matrix. At the organic-inorganic interface, several factors such as lattice geometry, polarity, stereochemistry and topography may act in concert to control nucleation and growth of crystals. Although several models have been proposed that discuss the significance of these factors for biomineralization, no comprehensive experimental data are available. In contrast to crystallization in exclusively inorganic systems, the kinetics of reaction and structural relationships between organic and inorganic phases in biominerals or biomimetic material is poorly understood. For example, it is not clear if the concept of epitactic growth (geometrical matching of unit cells at the interface of a secondary crystal growing on a primary crystal) applies to organic-inorganic systems. In contrast to inorganic templates that often have a smooth and rigid surface that promotes epitactic growth, biological substrates are usually rough and result in a large degree of mismatch. It is apparent that factors controlling the reaction at the crystal-matrix interface are strongly dependent upon the nature of the substrate. Therefore, characterization of the assembled organic surface and surface structure of the inorganic phase is crucial to understanding the processes of biomineralization. The focus of our research is the investigation of the processes leading to the nucleation and growth of crystals on both natural and synthetic systems through an interdisciplinary approach that integrates molecular biology, morphology and mineralogy using advanced preparation and analytical techniques. We have studied run-products, particularly magnetite, siderite and other carbonates, that resulted from extracellular biomineralization by extremophiles isolated from a variety of extreme environments ranging from permafrost to hydrothermal vent systems. The results of this study are critical to recognizing biomarkers in terrestrial and extraterrestrial environments.

Thomas-Keprta, Kathie↗

A TM Tasseled Cap equivalent transformation for reflectance factor data

A transformation of TM-waveband reflectance-factor data which provides features related as directly as possible to the corresponding TM Tasseled Cap brightness, greennes, and wetness features is presented. The reflectance factor transformation is based on spectrometer data integrated over the prelaunch composite-detector response functions of the Landsat-4 Thematic Mapper. A description, in general terms, of the approach for adjusting the transformation matrix to other types of reflectance factor data (different instrument or band response) is given.

Crist, E. P.↗

Factors influencing the Mode I interlaminar fracture toughness of a rubber toughened thermoplastic matrix composite

The use of a rubber modified thermoplastic resin has been investigated as a method to improve the Mode I interlaminar fracture toughness of a unidirectional continuous carbon fiber composite. Test results show that the improvement in the fracture toughness is less than expected due to rubber particle agglomeration, solvent and molding induced crystallization of the matrix and poor fiber/matrix adhesion. The plastic zone in composites utilizing tough matrices can extend well beyond a single interfibrillar spacing. However, the development of the plastic zone is limited due to the failure of the fiber/matrix interface. In order to fully evaluate the potential of tough composites using toughened matrices, any improvement made in the matrix toughness must be coupled with improvements in the fiber/matrix adhesion.

Parker, D. S.↗

Diagrammatic technique for calculating matrix elements of collective operators in superradiance

Adopting the so-called genealogical construction, one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicity the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes.

Lee, C. T.↗

Effect of molecular anisotropy on the intensity and degree of polarization of light scattered from model atmospheres

Computations of the properties of sunlight scattered from models of the earth-atmosphere system are presented to show the effect of molecular anisotropy on the intensity, flux, and degree of polarization of the scattered light. The values of these parameters change significantly when the anisotropy factor is neglected in the molecular optical thickness and scattering phase matrix. However, if the Rayleigh scattering optical thickness is kept constant and the molecular anisotropy factor is included only in the Rayleigh phase matrix, the flux does not change, the intensity changes by a small amount, but the changes in the degree of polarization are still significant.

Bahethi, O. P.↗

Superradiant effects on pulse propagation in resonant media

Adopting the so-called genealogical construction, the eigenstates of collective operators can be expressed corresponding to a specified mode for an N-atom system in terms of those for an (N-1)-atom system. Matrix element of a collective operator of an arbitrary mode is presented which can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME was obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups was then introduced. This gave a simple and systematic way of calculating the RME. Results show explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes and clears up the chief difficulty encounted in the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field.

Lee, C.↗

Darkening in gas-rich ordinary chondrites: Spectral modelling and implications for the regoliths of ordinary chondrite parent bodies

The dark fine grained matrix of gas-rich ordinary chondrites replicates many of the physical, morphological, and spectral characteristics of the highly shocked and optically altered black chondrites. Spectral mixture modeling shows that the darkening and spectral attenuation seen in the dark matrix can be simulated with realistic mass fractions of light host material and black chondritic material. All these factors point to the conclusion that the dark matrix of gas-rich ordinary chondrites is dark due to the same processes that darkens black chondrites, shock distributed small particle size FeNi metal and troilite. Because the darkening is not seen in any of the non-gas-rich light portions and is only seen in the gas rich grains of the meteorite, the shock darkening would have to occur as part of the matrix's exposure to regolith processes. Since all gas-rich grains are darkened, it follows that darkening is not only common, but pervasive in asteroidal regoliths. These results imply that the upper, optically active layer of an ordinary chondrite parent body should have the spectral characteristics of a black chondrite, which are a dark, relatively featureless spectrum with modest red slope in the infrared. These are the characteristics of special type C asteroids.

Britt, Daniel T.↗

A spatial operator algebra for manipulator modeling and control

A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

Rodriguez, G.↗

Fracture surface analysis in composite and titanium bonding

To understand the mechanical properties of fiber-reinforced composite materials, it is necessary to understand the mechanical properties of the matrix materials and of the reinforcing fibers. Another factor that can affect the mechanical properties of a composite material is the interaction between the fiber and the matrix. In general, composites with strong fiber matrix bonding will give higher modulus, lower toughness composites. Composites with weak bonding will have a lower modulus and more ductility. The situation becomes a bit more complex when all possibilities are examined. To be considered are the following: the properties of the surface layer on the fiber, the interactive forces between polymer and matrix, the surface roughness and porosity of the fiber, and the morphology of the matrix polymer at the fiber surface. In practice, the surface of the fibers is treated to enhance the mechanical properties of a composite. These treatments include anodization, acid etching, high temperature oxidation, and plasma oxidation, to name a few. The goal is to be able to predict the surface properties of carbon fibers treated in various ways, and then to relate surface properties to fiber matrix bonding.

Devilbiss, T. A.↗

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Korivi, V. M.↗

Modeling fatigue crack growth in cross ply titanium matrix composites

In this study, the fatigue crack growth behavior of fiber bridging matrix cracks in cross-ply SCS-6/Ti-15-3 and SCS-6/Timetal-21S laminates containing center holes was investigated. Experimental observations revealed that matrix cracking was far more extensive and wide spread in the SCS-6/Ti-15-3 laminates compared to that in the SCS-6/Timetal-21S laminates. In addition, the fatigue life of the SCS-6/Ti-15-3 laminates was significantly longer than that of the SCS-6/Timetal-21S laminates. The matrix cracking observed in both material systems was analyzed using a fiber bridging (FB) model which was formulated using the boundary correction factors and weight functions for center hole specimen configurations. A frictional shear stress is assumed in the FB model and was used as a curve fitting parameter to model matrix crack growth data. The higher frictional shear stresses calculated in the SCS-6/Timetal-21S laminates resulted in lower stress intensity factors in the matrix and higher axial stresses in the fibers compared to those in the SCS-6/Ti-15-3 laminates at the same applied stress levels.

Bakuckas, J. G., Jr.↗

Toughened Matrix SiC Fiber Reinforced Composites

First matrix cracking stress is a critical parameter for application of Sic fiber reinforced composites in highly stressed, environmentally demanding applications such as turbine blades. High matrix fracture toughness is a key property that contributes to high composite fracture stress. Silicon nitride offers reduced matrix elastic modulus, lower coefficient of thermal expansion, and potentially high fracture toughness compared to Sic matrices. All of these factors can be used to advantage to increase matrix fracture stress. As a first model system we are pursuing toughened silicon nitride matrix composites reinforced with SCS-9 fibers. Fabrication is by tape casting the matrix plies and tape lay-up with fiber plies followed by hot pressing at 1800 C. Progress toward this end will be reported.

Levine, Stanley R.↗

Semi-implicit transient analysis procedures for structural dynamics analysis

A semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid-body motions from element (or grid) to its adjacent elements.

Park, K. C.↗

An improved semi-implicit method for structural dynamics analysis

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.

Park, K. C.↗